I think you need groupby by first 3 chars of first column by str[:3] with mean:
df = df['Mkt-RF'].groupby(df['Unnamed:0'].str[:3]).mean()
Sample:
df = pd.DataFrame({'Unnamed:0':['192607','192608','193609','193610','193611'],
                   'Mkt-RF':[4,5,6,7,5]})
print (df)   
   Mkt-RF Unnamed:0
0       4    192607
1       5    192608
2       6    193609
3       7    193610
4       5    193611
#rename column
df = df.rename(columns={'Unnamed:0':'YEARMONTH'})
df = df['Mkt-RF'].groupby(df.YEARMONTH.str[:3]).mean().rename('MEAN').reset_index()
df.YEARMONTH = (df.YEARMONTH + '0').astype(int)
print (df)
   YEARMONTH  MEAN
0       1920   4.5
1       1930   6.0
Another solution is convert first to_datetime and groupby by year floor divided by 10:
df = df.rename(columns={'Unnamed:0':'YEARMONTH'})
df.YEARMONTH = pd.to_datetime(df.YEARMONTH, format='%Y%m')
df = df['Mkt-RF'].groupby(df.YEARMONTH.dt.year // 10).mean().rename('MEAN').reset_index()
df.YEARMONTH = df.YEARMONTH *10
print (df)
   YEARMONTH  MEAN
0       1920   4.5
1       1930   6.0